P surface = kPa P bottom = kPa F bottom = kN A block is sitting on a plate with

Question

Psurface =   kPa

Pbottom =   kPa

Fbottom =   kN

A block is sitting on a plate with surface area 0.29 m2 that
    is floating in a container of water that is 0.31-m deep and
    has a bottom area of 0.60 m2 as shown in the figure.
    The combined mass of the block and plate is 24 kg.
    Assume standard atmospheric pressure.     (a) What is the total pressure on the fluid just beneath the plate?

Psurface =   kPa

    (b) What is the total pressure at the bottom of the container if the water is 0.31 m deep?

Pbottom =   kPa

    (c) How much force does the fluid exert on the bottom of the container if its surface area is0.60 m2?

Fbottom =   kN

Explanation / Answer

a) mass = 24 Kg

Area = 0.29 m2

weight = mg = 24*9.8 = 235.2 N (down)

force due to air above = Po * A = 101325 * 0.29 = 29384.25 N (down)

force due to liquid below = PA = 0.29P N (upward)

For equilibrium

235.2 + 29384.25 = 0.29P

=> P = 102136 Pa = 102.136 kPa

Psurface = 102.136 kPa

b) Pressure at bottom = Po + density*g*height of water from surface to bottom = 101325 + 1000 * 9.81 * 0.31 = 104366 = 104.366 kPa

c) Force at bottom = pressure at bottom / area = 104366 / 0.6 = 173943 N = 173.943 kN

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